Bid for a chest without a top (5)
I believe the answer is:
offer
'bid' is the definition.
(I know that bid can be written as offer)
'a chest without a top' is the wordplay.
'a chest' becomes 'coffer' (coffer is a kind of chest).
'without a top' means to remove the first letter (in a down clue, top can mean the top letter).
'coffer' with its initial letter taken away is 'OFFER'.
'for' acts as a link.
(Other definitions for offer that I've seen before include "Make available for sale" , "Come up with" , "Suggest" , "Propose (to give)" , "Tender - proposal" .)